Gérard Houllier admitted Aston Villa are suffering a crisis of confidence after Liverpool ruined his return to Anfield with a commanding victory that left his team languishing two points above the relegation zone.

Villa slipped to their fourth consecutive defeat in all competitions and have won one of their last 10 league games under Houllier, as a Liverpool team minus Fernando Torres, Steven Gerrard and Jamie Carragher eased to eighth in the table with their fourth successive home league win. Houllier argued Liverpool's second goal, expertly converted by Ryan Babel, should have been disallowed for offside but conceded it occurred only because David Ngog's opening goal had a demoralising effect on his players.

"There are some areas that we have improved, such as changing the way we play and the way we approach the game, but once we go 1-0 down we need to be stronger mentally," Houllier said. "That's always been one of my main features [as a manager].

"The first goal affected out morale. We are not the most confident team and we are aware of that. We were on the back of three defeats so obviously the first goal stunned us. The second goal is offside and it's a vital goal as it means the game is over. After that it took us a while to get back into the game. We had a good start to the second half and nearly had a goal with the chance Gaby [Agbonlahor] had, but then we conceded a third goal on the break and that was it. We need to address a few problems. We were lacking too many things."

The former Liverpool manager was afforded a polite reception on his first competitive game back at Anfield since being dismissed in 2004, with the Kop briefly chanting his name in the final minutes. "I appreciated the fact they chanted my name at the end. That means they can remember," Houllier said. "There was a banner before the start of the game, too. I was not emotional but I was extremely touched by that. If I was going to lose 3-0 to anyone it would Liverpool, but at the same time I'm the boss of Aston Villa. If we'd scored at 2-1 the game would have been different."

Liverpool lost Torres just before kick-off when the striker's wife, Olalla, went into labour with their second child, a son. But there was no disruption to Roy Hodgson's team as José Reina became the quickest goalkeeper in the club's history to 100 clean sheets – achieving the feat in 198 league games compared to 217 by Ray Clemence – and Maxi Rodríguez completed the win with a fine breakaway goal.

"The most pleasing aspect was the team effort. The shape of the team was good throughout," Hodgson said. "It was more satisfying that so many players stepped up to the plate in the absence of our three most recognised starters in Gerrard, Torres and Carragher. We shot ourselves in the foot at the start of the season. We are still limping but the limp is getting better."